WIND. MILL. 



the vane a twift, and Co cauling each rib of the vane to lie 

 in a different plane. 



It is obferved, that the ribs of the vane or fail ought to 

 decreafe in length from the axis to the extremity, giving 

 the vane a curvilineal form ; fo that no part of the force 

 of any one rib be fpent upon the reft, but all move on 

 independent of each other. The twift above-mentioned, 

 and the diminution of the ribs, are exempHfied in the wings 

 of birds. As the end of the fail neareft the axis cannot 

 move with the fame velocity which the tips or fartheft ends 

 have, although the wind afts equally ftrong upon them, 

 Mr. Fergufon (Left, on Mechanics, p. 52.) fuggefts, that 

 perhaps a better pofition than that of ftretching them along 

 the arms direftly from the centre of motion, might be to 

 have them fet perpendicularly acrofs the farther ends of the 

 arms, and there adjufted lengthwife to the proper angle. 

 For, in that cafe, both ends of the fails would move with 

 nearly the fame velocity ; and being farther from the centre of 

 motion, they would have fo much the more power, and then 

 there would be no occafion for having them fo large as they 

 are generally made ; which would render them lighter, 

 and, confequently, there would be fo nuich the lefs 

 friftion on the thick neck of the axle, when it turns in the 

 wall. 



M. Parent confidered what figure the fails of a wind-mill 

 fhould have, to receive the greateft impulfe from the wind ; 

 and he determined it to be a feftor of an ellipfis, whofe 

 centre is that of the axis, or arbor, of the mill ; and the 

 little femi-axis the height of thirty-two feet : as for the 

 greater, it follows neceffarily from the rule that direfts the 

 fail to be inclined to the axis, in an angle of 55 degrees. 



On this foundation he alfumes four fuch fails, each of 

 which is one-fourth of an ellipfis ; which, he Ihews, will 

 receive all the wind, and lofe none, as the common ones do. 

 Thefe four furfaces, multiplied by the lever with which the 

 wind afts on one of them, exprefs the whole power the wind 

 has to move the machine, or the whole power the machine 

 has when in motion. 



The fame manner of reafoning, applied to a common 

 wind-mill, whofe fails are reftangular, and their length 

 about five times their breadth, fhews, that the eUiptic wind- 

 mill has about feven times the power of the common 

 one. 



A wind-mill with fix elliptic fails, he (hews, would ftill 

 have more power than one with only four. It would only 

 have the fame furface with the four, fince the four contain 

 the whole fpace of the ellipfis as well as the fix. But the 

 force of the fix would be greater than that of the four, in 

 the ratio of 245 to 231. If it were defired to have only 

 two fails, each being a femi-ellipfis, the furface would be 

 ftill the fame ; but the power would be diminifhed by near 

 one-third of that with fix fails, becaufe the greateft of 

 the feftors would much (horten the lever with which the 

 wind afts. 



Befl Form and Proportion of reSangular Wind- Mills 



As elliptical fails would be fomething fo new, that 

 there is little room to expeft they will come into common 

 ufe, the fame author has confidered which form, among the 

 reftangular ones, will be the moft advantageous. And by 

 the method de maximis et minimis, he finds it very different 

 from the common ones. 



The refult of this inquiry is, that the width of the reft- 

 angular fail (hould be nearly double its length ; whereas 

 the length is ufually made almoft five times the width. 

 Add, that as we call length the dimenfion which is taken 

 from the centre of the axis, the greateft dimenlion of the 

 new reftangular fail will be turned toward the axis, and the 



II 



fmalleft from it ; quite contrary to the pofition of the com- 

 mon fails. 



The power of a wind-mill with four of thefe new reft- 

 angular fails, M. Parent ftiews, will be to the power of four 

 elliptic fails, nearly as 1 3 to 23 ; which leaves a confiderable 

 advantage on the fide of the elhptic ones ; yet will the force 

 of the new reftangular fails be confiderably greater than that 

 of the common ones. 



M. Parent likewife confiders what number of the new 

 fails will be moft advantageous ; and finds, that the fewer 

 the fails, the more furface there will be, but the lefs 

 power. The ratio of the power of a wind-mill with fix 

 fails will be to another with four, nearly as 14 to 13. And 

 the power of another with four will be to that with two, 

 nearly as 13 to 9. 



For a variety of curious experiments and obfervations 

 concerning the conftruftion and efFefts of wind-mill fails, 

 by the ingenious Mr. Smeaton, fee Phil. Tranf. vol. ii. 

 p. 138, &c. 



Mr. Smeaton's experiments did not reali-ze M. Parent's 

 theory ; for he found the fails fixed at the angle of 55 de- 

 grees with the axis, to be the leail advantageous of any 

 which hp tried ; but if the fails are included from 72 to 7? 

 degrees from the axis, or 15 to 18 degrees to the place of 

 their motion, the greateft effeft will be produced that can 

 be when the fails are plane furfaces. 



He alfo found, that the elliptical fails, which intercept 

 the whole cylinder of wind, do not produce the great- 

 eft effeft, for want of proper interftices for the wind to 

 efcape. 



The following maxims, deduced by Mr. Smeaton from 

 his experiments, contain the moft accurate information upon 1 

 the fubjeft. 



Maxim I. — The velocity of wind-mill fails, whether un- 

 loaded or loaded, fo as to produce a maximum effeft, is ■ 

 nearly as the velocity of the wind, their ihape and pofition 

 being the fame. 



Maxim 2. — The load at the maximum is nearly, but : 

 fomewhat lefs than, as the fquare of the velocity of the 

 wind, the fhape and pofition of the fails being the fame. 



Maxim 3 The effefts of the fame fails at a maximum 



are nearly, but fomewhat lefs than, as the cubes of the velo- 

 city of the wind. 



Maxim 4. — The load of the fame fails at the maximum 

 is nearly as the fquares, and their effefts as the cubes of 

 their number of turns in a given time. 



Maxim 5 — When fails are loaded, fo as to produce a 

 maximum at a given velocity, and the velocity of the wind 

 increafes, the load continuing the fame : ift. The increafe 

 of effeft, when the increafe of the velocity of the wind is 

 fmall, will be nearly as the fquares of thofe velocities. 

 2dly, When the velocity of the wind is double, the effefts 

 will be nearly as 10 to 27I. But, 3dly, When the velo- 

 cities compared are more than double of that where the I 

 given load produces a maximum, the effefts increafe nearly I 

 in the fimple ratio of the velocity of the wind. 



Maxim 6. — In fails where the figure and pofitions are 

 fimilar, and the velocity of the wind the fame, the number 

 of turns in a given time will be reciprocally as the radius or 

 length of the fail. 



Maxim 7. — The load at a maximum that fails of a fimilar 

 figure and pofition will overcome, at a given diftaiice from 

 the centre of motion, will be as the cube of the radius. 



Maxim 8. — The effefts of fails of fimilar figure and pofi- 

 tion are as the fquare of the radius. 



Maxim 9. — The velocities of the extremities of the 

 fails, in all their ufual portions, when unloaded, or even 



loaded 



